import random
from fractions import Fraction
import math
from Solution import Solution

def is_green(speed, dist, dur):
    #print(speed, dist, dur)
    speed_sec = speed * Fraction(5,18)
    turn = math.floor(dist / (speed_sec * dur))
    return turn % 2 == 0

def max_speed(dists, t):
    if 0 in t:
        return 0
    l = []
    for i in range(len(dists)):
        l.append(sum(dists[:i+1]))
    #print(l)
    speed = 200
    while speed > 0:
        for i in range(len(t)):
            if is_green(speed, l[i], t[i]):
                if i == len(t) - 1:
                    return speed
            else:
                speed -= 1
                break
    return speed

def generate_question():
    nums = random.randint(1000, 9999)
    l = [random.randrange(100, 10000) for i in range(nums)]
    t = [random.randrange(1, 9999) for i in range(nums)]
    return l, t

def generate_nomal():
    nums = random.randint(10,50)
    l = random.sample(range(500, 5000, 10), nums)
    t = random.sample(range(10,60, 1), nums)
    return l, t

cases = []
cases.append([[1000], [18], 100])
cases.append([[1000], [15], 120])
cases.append([[500], [3], 150])
cases.append([[4375], [15], 175])
cases.append([[4825], [15], 193])
cases.append([[4930], [17], 174])
cases.append([[2500], [3], 187])
cases.append([[3000], [3], 200])
cases.append([[1910], [6], 191])
cases.append([[1815], [27], 121])
cases.append([[4560, 820, 1670, 780, 4270, 2150, 4440, 3520, 550, 4190], [39, 26, 54, 52, 30, 42, 56, 22, 36, 38], 181])
cases.append([[4070, 4780, 4650, 600, 4000, 3060, 1120, 3860, 4610, 4080, 2260], [24, 17, 26, 44, 50, 20, 39, 29, 15, 31, 54], 19])
cases.append([[1870, 4310, 3700, 1470, 2910, 1160, 3170, 3780, 1000, 2150], [39, 14, 33, 41, 25, 16, 31, 54, 17, 38], 41])
cases.append([[3100, 1380, 4690, 3760, 3630, 3180, 4960, 590, 4400, 2050, 1900, 2580], [29, 30, 46, 17, 27, 21, 50, 22, 43, 28, 36, 10], 44])
cases.append([[2840, 3600, 4090, 4470, 590, 2030, 1020, 1260, 1910, 4490], [12, 34, 58, 37, 36, 52, 45, 57, 27, 29], 142])
cases.append([[580, 4900, 3550, 560, 3940, 2060, 2410, 2330, 4530, 710, 3630], [37, 35, 47, 38, 16, 51, 19, 52, 36, 23, 15], 9])
cases.append([[540, 760, 1960, 2400, 1750, 1020, 1130, 690, 1330, 4620], [16, 42, 53, 46, 15, 10, 47, 25, 57, 36], 18])
cases.append([[2760, 4440, 1290, 2570, 3870, 1050, 3200, 3080, 2300, 2750, 1430, 3390, 2210, 2070], [43, 29, 55, 22, 25, 24, 34, 15, 49, 59, 18, 40, 33, 35], 89])
cases.append([[1910, 1690, 1680, 510, 3610, 970, 1870, 2360, 4980, 4690], [50, 28, 10, 16, 17, 41, 40, 15, 31, 36], 11])
cases.append([[4450, 2280, 870, 2010, 2670, 4600, 2540, 920, 1070, 4520, 3140, 3090, 2040], [43, 47, 28, 26, 25, 18, 12, 16, 39, 44, 27, 55, 34], 58])
cases.append([[1950], [27], 130])
cases.append([[2812, 8404, 7889, 6927, 7094, 6105, 9997, 149, 3949, 3076, 1019, 8317, 387, 7784, 5626, 7080, 1944, 956, 3625, 671, 7144, 5896, 7967, 9990, 9101, 5156, 5189, 2504, 785, 2642, 754, 3483, 107, 9729, 4876, 2581, 5229, 7177, 677, 1876, 784, 6827, 5282, 8164, 6399, 2143, 7528, 2386, 4907, 7303, 2126, 4352, 5744, 2439, 1001, 7496, 6281, 2500, 4225, 5162, 3005, 7018, 2513, 761, 6543, 5415, 5848, 2418, 5308, 9285, 9177, 5753, 7410, 6759, 8795, 8499, 934, 6777, 7765, 1082, 3266, 8394, 8242, 3232, 2993, 8284, 8589, 5129, 4925, 6075, 3407, 7251, 9017, 137, 810, 3197, 7438, 458, 9302, 4219, 1287, 194, 7304, 2966, 9146, 6152, 8412, 7974, 9394, 3852, 3361, 9807, 4203, 7165, 5960, 3904, 7042, 3926, 4553, 9153, 4523, 4531, 3255, 5915, 2030, 6882, 1099, 2017, 9569, 7187, 5713, 6889, 1714, 5615, 8396, 1738, 215, 4021, 6008, 3582, 2570, 1320, 7243, 490, 9810, 7706, 8282, 4816, 6122, 8115, 9855, 4524, 4459, 274, 6794, 3251, 746, 4700, 1213, 8578, 6175, 4260, 9006, 7890, 2778, 890, 6079, 6690, 151, 1808, 186, 1076, 9704, 1531, 8430, 5047, 9301, 5671, 9471, 8811, 8608, 4976, 656, 2738, 4795, 2830, 9497, 9756, 3856, 5323, 3822, 6288, 3695, 467, 2531, 4008, 9484, 4090, 7350, 556, 6189, 5853, 550, 5483, 5057, 127, 9670, 6677, 2873, 3072, 8768, 6973, 5817, 1802, 9465, 7126, 6193, 9080, 3202, 4754, 4215, 4421, 3529, 9268, 8414, 2449, 4288, 5866, 1038, 5812, 2971, 3452, 6260, 1379, 9823, 8633, 7336, 1509, 2525, 5142, 6256, 164, 6506, 3454, 7044, 8504, 4454, 2704, 5529, 2368, 9646, 9340, 5655, 4705, 6042, 9645, 8745, 7509, 5177, 8242, 3124, 5761, 2507, 4312, 8604, 6607, 5405, 9895, 3184, 7858, 9573, 185, 5977, 8013, 5715, 4840, 1751, 4772, 4055, 8126, 2392, 8765, 2839, 6422, 9817, 927, 5322, 3625, 4981, 980, 4036, 4774, 5785, 2807, 7047, 762, 6315, 7539, 7785, 9556, 6622, 6606, 884, 3060, 7178, 1674, 5256, 9269, 9923, 3508, 6404, 1644, 5953, 3578, 4437, 3002, 1622, 3781, 1996, 7684, 6798, 5984, 1195, 6224, 308, 889, 8587, 5534, 7453, 5311, 952, 2165, 715, 1595, 9122, 6815, 7371, 9945, 4809, 7043, 4368, 407, 5283, 5812, 8586, 2223, 3962, 4921, 3584, 2245, 9525, 5843, 631, 6023, 2102, 7678, 2551, 7525, 2660, 6209, 2290, 3247, 654, 6506, 3422, 5279, 6102, 4911, 8929, 8071, 4546, 3068, 141, 6003, 3389, 8320, 7203, 715, 1798, 7785, 5514, 1901, 9310, 3881, 4601, 3614, 6885, 2944, 8716, 2888, 6083, 3238, 3590, 4926, 3760, 3639, 3558, 7951, 8763, 8447, 6270, 7248, 3877, 940, 2474, 389, 1817, 7619, 2622, 9837, 4574, 1096, 143, 3615, 8519, 9114, 5185, 8703, 3228, 4466, 9848, 5704, 9161, 2555, 6989, 3544, 9355, 5372, 2830, 5766, 7184, 4781, 3909, 6179, 4306, 9841, 9472, 1453, 4638, 120, 4402, 8727, 5308, 3344, 3027, 8652, 6364, 6077, 1472, 3017, 1734, 4052, 7208, 7001, 9792, 202, 7162, 5129, 2346, 4599, 7611, 385, 4942, 7380, 6821, 5780, 7979, 1903, 9082, 9636, 416, 7476, 3863, 6304, 9287, 9367, 8889, 414, 711, 3217, 9784, 1502, 1082, 3742, 1495, 834, 6631, 5467, 8734, 2759, 8154, 1562, 3859, 8061, 8587, 5340, 4346, 7218, 1050, 5159, 2894, 5410, 2933, 2748, 5590, 7838, 2538, 366, 7501, 7505, 8860, 1041, 2594, 8170, 4379, 1755, 5467, 8035, 8655, 545, 6970, 7330, 6657, 8044, 8769, 4135, 5104, 9565, 5805, 1395, 2199, 4990, 1132, 6425, 5222, 7454, 5887, 4475, 1663, 9565, 999, 4630, 2442, 1504, 5588, 8581, 7947, 9383, 1676, 9022, 8751, 6790, 9523, 9404, 1465, 7436, 3928, 192, 6537, 7284, 1079, 4974, 4596, 9677, 3244, 9800, 8071, 4961, 3313, 2906, 7731, 4959, 9423, 6635, 3369, 3447, 3393, 9206, 8112, 4366, 4353, 9093, 4552, 5204, 3207, 9030, 4424, 2404, 2200, 9707, 2886, 8382, 3982, 461, 5207, 959, 5368, 3380, 1047, 7502, 5030, 234, 3681, 1629, 7883, 4648, 2102, 854, 3134, 7654, 3334, 9768, 9132, 3418, 5685, 8892, 3250, 6537, 6366, 9642, 3018, 7654, 9460, 3763, 6004, 9275, 7734, 1801, 927, 2123, 9125, 958, 3140, 6709, 6420, 9206, 2316, 2024, 8484, 7176, 416, 3753, 4782, 5614, 3865, 4939, 8087, 7177, 6799, 5848, 9895, 5716, 8403, 3083, 5780, 9116, 1513, 6021, 2217, 6355, 9167, 9466, 8946, 797, 8404, 6431, 9561, 9217, 5404, 6418, 1282, 9455, 3714, 6606, 4012, 2437, 3366, 4387, 5581, 178, 9803, 2805, 6078, 5865, 1485, 2475, 8688, 6075, 418, 4153, 4815, 1941, 3021, 4623, 2505, 2651, 2093, 5174, 7093, 9857, 5513, 5654, 129, 8874, 4025, 5229, 4100, 6692, 1230, 1117, 9938, 4140, 1947, 8524, 1223, 8420, 6545, 9780, 787, 5435, 8306, 741, 9149, 5252, 5786, 7052, 5381, 9304, 9113, 1803, 1924, 1203, 3322, 4550, 3472, 7344, 5665, 8240, 7374, 3167, 2741, 8674, 5121, 7388, 2182, 3149, 1620, 8722, 5049, 1111, 3121, 5548, 8802, 3713, 248, 4880, 7345, 921, 2963, 8917, 7780, 3056, 8166, 2432, 9852, 451, 5121, 5166, 6233, 3671, 2488, 4988, 7364, 9320, 6927, 302, 9475, 9308, 4461, 4799, 3108, 7817, 6198, 4803, 2093, 1248, 6767, 641, 6281, 7500, 9441, 4126, 419, 9865, 9792, 3342, 1658, 7707, 3187, 6557, 2348, 2755, 1354, 9907, 7723, 1704, 1685, 1781, 2051, 2082, 649, 2997, 2191, 4044, 8057, 8383, 1324, 870, 2551, 417, 3806, 9313, 7948, 341, 9770, 9920, 3817, 1788, 2886, 9004, 7666, 5394, 799, 8115, 4439, 1715, 1416, 4811, 8768, 7126, 2379, 2561, 3006, 3456, 5862, 775, 4170, 7601, 4740, 1951, 6012, 9647, 6817, 9023, 9624, 1380, 7160, 5460, 7884, 8909, 4347, 6432, 8502, 8358, 3845, 3377, 8483, 995, 1934, 613, 524, 9102, 2436, 2506, 3279, 3465, 8061, 7435, 6823, 8125, 1353, 4272, 8813, 9567, 9997, 2591, 2671, 9897, 3832, 3927, 1073, 1113, 2447, 3831, 1308, 3833, 1636, 6676, 6823, 9451, 9705, 8203, 4008, 9893, 111, 4595, 2315, 1950, 1474, 4922, 5994, 5374, 4428, 3899, 8090, 6372, 8525, 9696, 7078, 5059, 1561, 5148, 1426, 7499, 8584, 9281, 4673, 5228, 2103, 2318, 3510, 699, 820, 6040, 5770, 6921, 323, 6017, 5849, 2993, 5264, 6462, 9227, 2228, 2058, 1476, 2294, 3117, 5746, 7763, 4068, 8701, 9706, 9207, 3609, 3035, 1192, 5573, 9528, 1286, 6002, 2796, 600, 4433, 5073, 6747, 9448, 1480, 1067, 481, 3051, 2364, 7252, 9118, 5036, 5783, 2306, 6733, 9054, 2869, 6682, 1058, 4928, 6701, 964, 1066, 8751, 5437, 6637, 6206, 8648, 5954, 9169, 7998, 6624, 4979, 197, 9376, 1673, 7623, 4741, 4697, 1490, 4294, 9800, 8347, 9174, 153, 1517, 6985, 9039, 5931, 500, 4190, 1204, 7352, 3109, 7632, 7043, 1489, 7423, 3337, 2655, 4847, 7887, 4047, 596, 3087, 8320, 2780, 3252, 4134, 8283, 5616, 3826, 249, 1656, 2699, 4518, 6448, 1333, 795, 6078, 6631, 4555, 2694, 988, 2480, 4289, 4613, 3976, 7409, 4296, 7900, 1206, 6243, 7636, 1581, 7762, 9517, 8426, 3765, 747, 4709, 583, 2000, 428, 6521, 5769, 8868, 2342, 8992, 9057, 6957, 6776, 8170, 8220, 4493, 2172, 3108, 590, 834, 4346, 5510, 9328, 5685, 7541, 4934, 8737, 2830, 8292, 3026, 4673, 5072, 3195, 4603, 3295, 6049, 8570, 6041, 3583, 2247, 9403, 7111, 722, 450, 7892, 9711, 9180, 4195, 8307, 3382, 6417, 5278, 7285, 2643, 8632, 4854, 1190, 3811, 8954, 319, 3185, 7526, 4912, 6353, 3263, 9270, 8844, 7389, 6524, 3300, 1667, 3549, 2028, 8371, 4491, 1886, 7906, 6428, 2768, 9836, 5013, 4478, 5746, 3116, 6050, 3865, 2217, 4004, 1342, 1984, 4942, 2354, 5998, 6557, 7723, 5286, 3083, 8777, 4573, 1382, 5398, 6405, 3573, 5330, 697, 7027, 4488, 4457, 6189, 7008, 3743, 6244, 5301, 9176, 6128, 842, 1482, 9188, 5762, 8601, 7248, 9679, 8635, 1094, 9105, 6767, 8604, 4821, 3057, 5863, 2193, 6700, 1450, 4512, 4509, 8761, 4138, 8762, 3539, 7624, 7375, 4765, 1000, 8747, 8307, 8179, 1586, 4480, 3837, 7361, 289, 5440, 4484, 7642, 2667, 8800, 1408, 2063, 4493, 2596, 5350, 9684, 2989, 7109, 6188, 5815, 8051, 2669, 6261, 5912, 739, 4560, 6542, 2665, 3559, 7903, 4946, 9091, 2631, 8101, 7008, 310, 8622, 2004, 5207, 535, 2082, 1541, 9575, 2915, 8631, 8669, 4667, 369, 2423, 9613, 9292, 8359, 2013, 4227, 5114, 2285, 4748, 8857, 8295, 5253, 2055, 1743, 757, 6580, 5768, 4483, 4697, 724, 7708, 8538, 4877, 6606, 1757, 2699, 7259, 6751, 3117, 8028, 2469, 1175, 909, 7421, 4618, 7376, 8593, 5456, 463, 3119, 1528, 7532, 6443, 3826, 9999, 5136, 4271, 4679, 5224, 6898, 5494, 199, 1218, 8107, 2984, 769, 6902, 7703, 1709, 7225, 8342, 8166, 3368, 162, 2701, 866, 6144, 6002, 8932, 9515, 8303, 4430, 1589, 8548, 705, 7593, 936, 9318, 9273, 2019, 9189, 6319, 3692, 5073, 4459, 5265, 5173, 2248, 7223, 8777, 3797, 2010, 8409, 9679, 9453, 6531, 5733, 9630, 376, 2137, 5285, 934, 1421, 1915, 2647, 8674, 315, 202, 9309, 9607, 4860, 6008, 1381, 912, 1324, 5889, 7704, 1239, 4996, 6636, 9151, 6637, 3088, 3846, 4368, 2583, 5609, 9816, 1553, 8673, 8139, 243, 6886, 456, 8267, 8211, 920, 7302, 8368, 878, 889, 2306, 7592, 7770, 7015, 4964, 4175, 2297, 8999, 5399, 9235, 8543, 959, 5757, 5948, 3080, 3968, 7954, 3548, 8777, 2023, 782, 2346, 3731, 6652, 2118, 1180, 2444, 1244, 2082, 443, 2440, 405, 1994, 9244, 2574, 7928, 6176, 9677, 4343, 1651, 9778, 7472, 5349, 2238, 3405, 4577, 2621, 1109, 8468, 1875, 6867, 5011, 8141, 8314, 5368, 4096, 5660, 1907, 2465, 1205, 9318, 2931, 9233, 7822, 1955, 6867, 7433, 1471, 4651, 3819, 2534, 6014, 7233, 5110, 3898, 1328, 3340, 5591, 2362, 6002, 3287, 6356, 2715, 7229, 4629, 1129, 8092, 510, 8919, 9410, 5820, 1423, 1524, 7403, 9530, 2336, 1615, 9625, 7116, 5928, 6286, 2432, 9677, 7381, 3851, 4299, 3789, 1200, 7065, 4303, 2811, 1919, 473, 7362, 9382, 4936, 1724, 5147, 1328, 8658, 9090, 5807, 8939, 9767, 7214, 2605, 8942, 7610, 9377, 7313, 7837, 6546, 580, 4580, 6779, 9199, 3815, 6484, 6827, 8621, 2485, 8254, 1427, 4801, 5689, 6205, 3946, 5015, 5376, 6525, 9935, 1939, 8126, 9202, 2954, 7779, 3787, 3122, 4411, 763, 4711, 9056, 6332, 3520, 7765, 1193, 3609, 4667, 4522, 3282, 3528, 6250, 8771, 9212, 8713, 4394, 8970, 3190, 8734, 4308, 8928, 5724, 784, 7290, 1062, 2255, 5614, 9555, 8045, 172, 1594, 5990, 4731, 2476, 7868, 6833, 6400, 1237, 7851, 6488, 1910, 5954, 7432, 1776, 2973, 9976, 6917, 9702, 5311, 3501, 4943, 3295, 1151, 1946, 2241, 4136, 5464, 3620, 402, 1193, 7771, 1936, 343, 7293, 924, 7400, 631, 9796, 2132, 533, 4225, 2659, 2338, 5752, 9234, 4486, 1734, 375, 3327, 2895, 9231, 8758, 5604, 1422, 6186, 6051, 7985, 9929, 7188, 8172, 8126, 2998, 3545, 833, 933, 4146, 4576, 9669, 2972, 553, 6017, 9229, 5855, 9499, 8597, 4182, 912, 6080, 6933, 2892, 7763, 3492, 4943, 3959, 1441, 977, 5699, 3301, 5808, 7067, 8451, 9495, 3874, 7604, 5082, 8196, 3178, 7969, 5681, 3235, 2725, 3732, 404, 4309, 1235, 1093, 3637, 2033, 2307, 7412, 1445, 2274, 9803, 860, 2435, 5879, 1646, 7468, 5564, 6376, 3197, 3851, 5982, 1426, 9176, 7322, 8509, 9368, 8543, 4012, 1575, 2257, 243, 9371, 1916, 5628, 9754, 5405, 3370, 5799, 4773, 4897, 3428, 7366, 3105, 3198, 3848, 8672, 7383, 2714, 1940, 4993, 5954, 6642, 9178, 7432, 2675, 1783, 4013, 6139, 5972, 2423, 3743, 488, 9133, 5414, 2438, 6067, 7073, 3512, 2224, 2515, 3359, 4057, 8783, 3125, 5192, 7991, 1565, 9498, 9086, 5301, 9786, 8810, 8742, 4870, 3706, 5146, 6823, 5387, 2121, 3425, 7426, 2966, 9526, 6125, 3925, 9784, 2617, 3646, 7121, 9839, 2035, 3970, 7539, 180, 4008, 9188, 3615, 5281, 3907, 2275, 728, 7121, 7090, 1640, 6255, 4537, 4436, 533, 9249, 9945, 1725, 285, 7797, 4187, 5660, 4421, 7723, 5699, 6533, 2415, 2846, 7331, 9161, 7042, 7733, 6068, 6973, 3479, 5765, 191, 3986, 4619, 2952, 9135, 1431, 4420, 1496, 3333, 6477, 809, 8191, 1551, 2485, 272, 4259, 8367, 3415, 964, 4451, 4242, 6823, 7831, 2552, 8122, 8713, 1524, 148, 2338, 3424, 3679, 1662, 7127, 6896, 223, 2041, 199, 3652, 9845, 287, 4728, 7717, 8900, 1345, 3466, 9331, 8048, 1252, 6704, 2239, 6488, 4662, 2025, 2742, 6484, 1419, 7929, 3536, 1056, 9403, 4985, 5736, 7171, 544, 595, 8231, 4369, 5758, 2539, 4993, 3369, 4806, 3948, 4900, 3441, 6828, 8406, 6620, 1912, 1569, 7687, 5725, 3902, 888, 7451, 956, 7973, 6061, 1905, 5839, 6070, 6148, 5764, 9750, 2803, 7705, 2731, 8218, 4129, 2408, 1554, 5454, 1614, 581, 4414, 8785, 8770, 5655, 9219, 8682, 7876, 7719, 6663, 3704, 6160, 4131, 5107, 3561, 2858, 5694, 1683, 8869, 1728, 3732, 906, 1982, 3749, 6705, 7503, 3918, 1024, 4569, 6507, 8804, 2846, 1147, 1125, 3943, 7289, 2297, 4149, 910, 5729, 5959, 2620, 7750, 226, 308, 1636, 9153, 3504, 3443, 151, 593, 2253, 2653, 1083, 1897, 9460, 844, 8510, 6542, 9154, 8527, 2053, 8671, 9214, 5241, 9651, 3453, 8031, 1724, 1531, 5549, 8310, 4604, 6496, 9169, 6626, 5897, 8426, 192, 7008, 4807, 4792, 7574, 4564, 9697, 4925, 9840, 5749, 2552, 8088, 9307, 448, 3649, 8068, 4384, 222, 1338, 3777, 7759, 5574, 8072, 9709, 2728, 649, 9852, 559, 8976, 9596, 1848, 8230, 7643, 2804, 5069, 9376, 8489, 7852, 9570, 2377, 796, 2773, 4198, 2915, 6316, 453, 9191, 4342, 5655, 7575, 6643, 8886, 5371, 2231, 4474, 1589, 7039, 6632, 1851, 3531, 8749, 9835, 8154, 6610, 1232, 9646, 9360, 5980, 7008, 599, 9905, 128, 2217, 4788, 1514, 1700, 8953, 6086, 6423, 7929, 7976, 6403, 7352, 9194, 8296, 6578, 4554, 7040, 4574, 247, 1436, 6157, 866, 9026, 5565, 5387, 1846, 6495, 1921, 6704, 8012, 5559, 5404, 8409, 7129, 165, 4402, 6127, 4840, 7374, 2126, 250, 792, 2205, 3224, 3897, 1392, 108, 8870, 399, 5889, 1517, 9077, 5699, 734, 3463, 7236, 7648, 8465, 8214, 6776, 3878, 9207, 147, 7530, 1788, 9868, 1829, 8012, 3892, 3144, 2142, 7459, 3468, 3134, 5664, 4192, 2514, 9253, 7175, 3404, 5267, 5478, 1333, 8047, 9327, 2843, 1808, 2191, 2473, 3384, 872, 3865, 803, 3336, 7296, 581, 1743, 9118, 9336, 3389, 1396, 9201, 4834, 8607, 1328, 457, 3081, 6789, 9817, 2333, 8169, 4422, 3228, 7600, 578, 7962, 1077, 5412, 1660, 4082, 5727, 5495, 4389, 7783, 1469, 5891, 2144, 7447, 9667, 8931, 7841, 4053, 1429, 1776, 6954, 8000, 4135, 4479, 5299, 4869, 7800, 4190, 4521, 151, 7910, 690, 4112, 3710, 1965, 1931, 305, 3539, 781, 8910, 9597, 7008, 6776, 6685, 6960, 8957, 1932, 249, 6320, 8776, 4476, 863, 2424, 6537, 8268, 8259, 7725, 8056, 7196, 5778, 6248, 4890, 9027, 231, 7704, 4890, 5106, 825, 4194, 774, 295, 2921, 3839, 3753, 7643, 3484, 9833, 9207, 5731, 8489, 9596, 3158, 5005, 9188, 1879, 9226, 9801, 4015, 1036, 8177, 3473, 1131, 3244, 2771, 4142, 7817, 8915, 5349, 2583, 5006, 6724, 4661, 5224, 1057, 973, 2491, 634, 5074, 6450, 512, 5518, 5714, 1561, 5577, 9178, 7715, 4133, 3114, 4519, 9158, 9772, 1027, 8152, 6266, 5566, 7857, 5147, 9300, 8791, 8858, 6120, 7506, 5160, 6568, 9121, 878, 9188, 1735, 8434, 2467, 9144, 9324, 2437, 5740, 1958, 8141, 1022, 9097, 6653, 1696, 5064, 6931, 1520, 3350, 6652, 2946, 6975, 8163, 5538, 1510, 3103, 8793, 6396, 5248, 2029, 3108, 5409, 752, 4937, 7741, 9875, 3377, 4740, 8402, 294, 2739, 7277, 2092, 6910, 6749, 4686, 4943, 7041, 8578, 9941, 6278, 1346, 5370, 7164, 3975, 6164, 1925, 639, 9413, 6080, 8660, 440, 8058, 7038, 4206, 7068, 2959, 7717, 7751, 5877, 7952, 2459, 2980, 2556, 5810, 7215, 4752, 2611, 3981, 7890, 5376, 4899, 3810, 5615, 2041, 8395, 5939, 8135, 887, 7328, 7670, 928, 3298, 164, 5152, 7428, 7414, 7921, 7946, 209, 3491, 208, 3616, 3827, 8096, 7444, 3103, 2894, 2073, 2412, 4683, 3815, 9562, 6176, 9906, 7344, 1660, 1553, 5640, 1956, 825, 1066, 7728, 6136, 5510, 9142, 8175, 9655, 1728, 7745, 775, 1855, 5493, 2241, 6718, 2555, 5127, 8637, 9428, 260, 9527, 6227, 1551, 3567, 1843, 489, 904, 7923, 9900, 3865, 6087, 8368, 1280, 9360, 5202, 6949, 1331, 7241, 688, 7997, 5541, 4860, 8952, 960, 2373, 6220, 1703, 6341, 4677, 3194, 9059, 1245, 2857, 1030, 7094, 552, 6484, 6939, 7417, 4003, 2645, 533, 7568, 5810, 4295, 2231, 697, 8168, 1074, 3308, 2681, 199, 1244, 8184, 9731, 856, 2854, 9075, 4342, 8291, 8026, 6025, 8298, 1530, 1754, 9512, 8056, 4863, 2037, 9476, 2055, 3623, 9010, 3919, 5494, 4276, 3082, 5452, 2922, 9370, 7058, 1085, 3832, 1026, 7362, 764, 535, 6867, 4939, 6154, 7085, 5631, 492, 5376, 9241, 8494, 1298, 3935, 7873, 9376, 8325, 7671, 2107, 8930, 5922, 1601, 7125, 7020, 3865, 1397, 5294, 3990, 3955, 7014, 7200, 6886, 4549, 774, 613, 619, 5323, 7039, 4301, 6129, 1473, 7721, 9755, 9368, 2637, 2214, 2332, 5601, 4983, 9937, 5020, 8362, 7492, 6323, 139, 1064, 2630, 3767, 699, 5456, 3246, 9997, 4129, 4868, 1733, 5301, 9452, 5400, 6347, 9532, 7150, 4360, 4876, 9575, 4840, 6733, 1067, 4451, 9611, 2835, 816, 8205, 8857, 6898, 9370, 6011, 6339, 3982, 1651, 7296, 6867, 6775, 7133, 3780, 7123, 720, 6627, 4123, 7747, 8042, 8674, 1621, 9253, 3726, 7516, 7826, 2975, 1922, 2797, 8009, 4639, 7373, 5590, 4095, 2626, 2090, 3017, 8641, 8009, 3714, 6601, 611, 3231, 6696, 3662, 6182, 123, 3569, 8262, 4183, 6553, 4998, 5834, 6582, 8043, 5021, 2786, 5382, 6697, 940, 6405, 1971, 1673, 2259, 7248, 8373, 1073, 7960, 1097, 3310, 8134, 6680, 4075, 4109, 1984, 4278, 9301, 5719, 9933, 2707, 4100, 8373, 7625, 8494, 7512, 5666, 7161, 7839, 3246, 5325, 6593, 4285, 9571, 8930, 7930, 1702, 3796, 3203, 7368, 9676, 9465, 4656, 5787, 1821, 3458, 587, 3512, 1073, 5515, 3308, 8088, 2918, 1376, 8888, 1204, 639, 2539, 1155, 1056, 8168, 5443, 8481, 4052, 2677, 6241, 1352, 8183, 365, 4424, 1012, 3553, 9916, 7726, 5679, 9440, 7799, 1091, 9884, 7101, 9623, 8555, 7069, 7504, 7830, 5553, 4189, 6888, 9580, 5691, 3617, 9977, 7284, 3149, 9691, 2622, 5803, 2525, 5342, 1086, 2332, 7196, 2586, 7140, 1971, 6813, 2911, 6030, 3365, 5526, 6715, 5094, 8054, 6065, 9657, 9778, 8727, 2893, 4031, 6555, 409, 8891, 3341, 9511, 9460, 6353, 1353, 5692, 1544, 4025, 3331, 9380, 3721, 1255, 4466, 2272, 2209, 7883, 8290, 4971, 7560, 9961, 7972, 8273, 5222, 4767, 9839, 9491, 2764, 9154, 9091, 8101, 3470, 2768, 1523, 6690, 6331, 6847, 1437, 3268, 4167, 8090, 7279, 8030, 9648, 515, 589, 7373, 9838, 3053, 5723, 1137, 1924, 2674, 7931, 775, 374, 1711, 3247, 4092, 8406, 1991, 3034, 7967, 7196, 2180, 2914, 2184, 636, 6681, 5674, 3238, 5902, 1727, 6538, 3540, 7493, 2863, 2422, 6870, 7069, 264, 774, 9658, 8524, 1741, 6070, 5282, 3336, 6977, 7654, 9341, 9005, 112, 6953, 7263, 1917, 6036, 1716, 2297, 3454, 1852, 2932, 6109, 4052, 3951, 7794, 5753, 768, 6915, 2984, 5115, 6491, 1321, 2479, 6758, 6960, 8202, 8248, 1290, 3586, 9227, 2183, 514, 7536, 3007, 9938, 5465, 6755, 5869, 7213, 7896, 4405, 2653, 7567, 9260, 7998, 4642, 3610, 8142, 8861, 7391, 1713, 1927, 1537, 1716, 8489, 1426, 5224, 540, 9508, 1830, 698, 951, 4270, 9063, 2533, 6219, 4729, 6861, 7664, 2548, 1773, 3817, 1908, 9214, 8652, 1695, 8942, 8998, 3676, 6350, 2079, 4039, 8706, 9681, 6190, 7992, 8035, 1635, 7747, 5115, 3335, 6810, 1125, 4878, 4317, 8889, 657, 6571, 9025, 5649, 3675, 1851, 9353, 8549, 5781, 7356, 8425, 6800, 4258, 5408, 7855, 5333, 1546, 429, 2819, 1660, 8918, 1193, 9198, 8725, 1615, 6967, 6289, 9737, 6411, 257, 8887, 1125, 1505, 9169, 411, 5857, 6698, 2141, 2507, 427, 5233, 8737, 2213, 6363, 6747, 2089, 4464, 8859, 8307, 4641, 6740, 7794, 240, 4591, 9828, 9569, 341, 8272, 5904, 1300, 3568, 564, 456, 9733, 6102, 359, 1580, 5959, 9150, 8361, 8914, 5630, 8558, 3001, 3199, 7787, 2939, 1860, 9698, 5575, 5579, 443, 1589, 7518, 6059, 4196, 9462, 5915, 4432, 7810, 7445, 2458, 9602, 4208, 403, 628, 8907, 9105, 4927, 4540, 8741, 1305, 869, 8573, 7456, 4982, 9302, 8527, 4879, 3152, 3700, 7663, 574, 7045, 2858, 861, 9195, 471, 3104, 359, 5632, 5944, 899, 7544, 3163, 6555, 1155, 283, 2359, 6744, 4792, 556, 8427, 7656, 8980, 4245, 3122, 4219, 6581, 9435, 9629, 2826, 6810, 1289, 3575, 940, 8777, 287, 9666, 2442, 8134, 1300, 5161, 7435, 5219, 1305, 8754, 6193, 8837, 9794, 9522, 1320, 7337, 5203, 5240, 712, 281, 9585, 3425, 5687, 8035, 6043, 327, 214, 2536, 2274, 7369, 2269, 589, 9594, 7555, 9902, 6436, 9254, 6171, 6705, 3449, 6651, 504, 1396, 897, 5248, 2654, 1689, 3278, 3292, 9638, 3112, 4047, 235, 4810, 1848, 7693, 6956, 9578, 6531, 3971, 6353, 4090, 3336, 3724, 1755, 3995, 8123, 9072, 4090, 5561, 6081, 4186, 7033, 4795, 6582, 7547, 4423, 831, 5522, 4723, 4615, 1622, 9741, 1121, 9090, 3652, 1752, 4962, 7765, 5809, 4308, 3173, 2470, 334, 259, 6600, 4161, 827, 5377, 5978, 9827, 199, 2440, 7880, 8578, 5058, 143, 8375, 647, 6444, 6957, 1757, 1303, 2069, 2019, 6305, 109, 7101, 3461, 2956, 5842, 1068, 1896, 8749, 1408, 1480, 3835, 1971, 486, 2040, 8396, 3802, 1625, 5693, 1839, 5243, 6261, 1092, 5042, 1272, 8577, 2234, 6260, 7815, 7782, 2732, 6337, 966, 5050, 7196, 3603, 5450, 169, 1182, 4818, 642, 4117, 8685, 4157, 2605, 1266, 5667, 6949, 9619, 6750, 3066, 5049, 932, 6074, 164, 212, 6192, 1922, 1875, 6354, 6583, 9701, 3580, 8946, 4529, 2120, 3788, 1357, 2201, 4457, 7535, 6277, 4436, 8908, 8134, 8646, 5291, 196, 8209, 8027, 9576, 5474, 8425, 3715, 5152, 4181, 8268, 2103, 509, 5947, 3207, 8473, 6385, 3155, 7768, 8441, 8529, 8328, 5511, 1224, 578, 9470, 762, 6578, 1485, 9354, 1448, 1132, 7642, 6946, 6823, 8802, 4919, 8173, 7310, 9790, 6336, 9364, 3443, 6519, 9946, 9512, 4495, 6306, 3773, 419, 396, 105, 8478, 810, 5466, 7285, 7491, 5070, 2867, 6547, 2376, 5999, 8749, 3736, 4988, 6590, 3458, 9098, 5642, 9063, 5851, 5068, 5636, 3475, 2980, 2126, 5146, 3628, 5305, 4834, 2136, 6217, 6381, 8936, 5504, 337, 3756, 8922, 4556, 6584, 8965, 9960, 7369, 3416, 6113, 4943, 6723, 3823, 9404, 211, 4142, 4243, 7634, 2275, 3033, 4648, 7512, 8596, 5983, 5799, 4234, 9664, 742, 8447, 8663, 2147, 3373, 720, 380, 3748, 2986, 1532, 4266, 4782, 7372, 8132, 3619, 9254, 3887, 3720, 2777, 1734, 4855, 3240, 1703, 6437, 3034, 9026, 979, 7452, 1027, 4471, 3694, 5124, 1479, 3794, 399, 4411, 906, 6010, 9097, 4271, 3277, 2344, 8251, 3936, 5590, 9138, 7119, 5169, 4568, 4699, 7647, 3146, 5940, 3849, 4887, 8252, 6825, 9681, 3752, 6244, 2927, 5444, 167, 3067, 7623, 4409, 8625, 1173, 1945, 6743, 1999, 7768, 5105, 3065, 4629, 2876, 2790, 4514, 2171, 1634, 8792, 8222, 9413, 6866, 4848, 7211, 5215, 7870, 6393, 1916, 3914, 2120, 1995, 8113, 8334, 8604, 2123, 6084, 608, 3156, 3321, 7740, 3336, 669, 4350, 2495, 4790, 1496, 9945, 4914, 6104, 1347, 9619, 7013, 6472, 7481, 4251, 7356, 1252, 422, 2740, 4760, 4566, 3426, 3744, 3354, 7921, 5163, 646, 6420, 9523, 1274, 5447, 532, 4315, 8389, 6264, 8057, 4118, 5418, 8800, 9194, 5321, 4977, 2019, 7854, 8984, 9901, 3533, 5336, 725, 6318, 4456, 8815, 7105, 960, 2237, 2681, 6971, 7757, 1797, 3064, 1064, 2045, 3665, 4818, 2249, 9437, 436, 5376, 5172, 2201, 2017, 5232, 4553, 9610, 6688, 532, 836, 9644, 3284, 2298, 8698, 1189, 8747, 8932, 2592, 2953, 3611, 252, 9384, 8732, 5462, 3420, 8061, 9177, 437, 2341, 4141, 7047, 2471, 2590, 753, 2754, 5764, 3117, 9089, 9911, 6972, 8851, 2107, 5293, 6181, 6362, 6029, 4551, 5260, 5261, 1987, 9491, 3940, 1512, 1040, 4170, 1992, 6660, 8671, 3913, 1388, 1497, 4215, 6978, 9755, 9664, 1829, 6783, 5640, 9040, 1752, 8761, 107, 1835, 730, 2551, 5226, 4702, 9364, 8691, 2568, 7157, 5772, 7384, 1706, 6641, 9541, 7074, 8927, 8657, 8043, 8816, 6401, 9131, 9030, 567, 7783, 8546, 7074, 2241, 3970, 2647, 8039, 6467, 5061, 3371, 8638, 6478, 7641, 1721, 6182, 2520, 8350, 1203, 7270, 2518, 6436, 2133, 5774, 3962, 4452, 4759, 319, 6338, 5274, 9096, 5614, 2221, 4728, 7877, 9021, 3749, 7572, 1362, 1569, 906, 8157, 5215, 7046, 4973, 3120, 6482, 1506, 8749, 6029, 7150, 5353, 8517, 9545, 7069, 154, 2733, 2048, 5333, 1417, 692, 5393, 7121, 5175, 6435, 9798, 3657, 7697, 874, 7541, 8930, 1273, 9009, 3248, 4920, 6161, 5950, 1948, 9142, 1951, 3362, 1946, 2997, 5891, 7019, 3762, 3080, 8861, 6413, 3361, 4647, 4416, 6919, 1612, 7329, 1752, 7228, 4017, 860, 3721, 2102, 1256, 796, 7907, 4997, 265, 6494, 7186, 8958, 6302, 3233, 1180, 9129, 2625, 8365, 5426, 5381, 9737, 4798, 7180, 5201, 8553, 7927, 5312, 3339, 3067, 1475, 9717, 8617, 1981, 8823, 5598, 1789, 5703, 2796, 4805, 3468, 2724, 5194, 7312, 1137, 242, 3487, 3869, 2566, 8029, 9336, 5850, 8450, 6315, 3071, 588, 3037, 4320, 4250, 2465, 6979, 2677, 4329, 7294, 3384, 2471, 7220, 9261, 943, 8060, 3275, 6628, 5292, 9147, 4268, 3853, 9100, 2099, 6728, 2577, 3580, 2088, 1546, 4212, 1139, 222, 6874, 5164, 4383, 9166, 5416, 5710, 3926, 7599, 2207, 211, 1611, 6143, 2745, 3474, 1758, 3364, 8582, 5048, 5096, 7702, 6257, 6548, 1723, 523, 8908, 7090, 9513, 3144, 4506, 9670, 5896, 7401, 474, 3759, 9921, 6799, 1273, 8630, 4296, 9511, 9382, 472, 8067, 1712, 705, 2347, 4044, 6840, 7095, 6251, 5225, 563, 3919, 6253, 8339, 426, 6159, 4210, 7319, 7830, 3025, 926, 4421, 2940, 7381, 2669, 1493, 4896, 1730, 4836, 6793, 1793, 3529, 7194, 1254, 934, 535, 8513, 939, 2981, 8241, 3131, 4058, 1046, 5860, 7868, 8702, 3084, 9267, 4765, 7502, 3683, 5902, 4696, 5619, 5881, 5631, 273, 8333, 8799, 3991, 198, 9760, 741, 9556, 7139, 2596, 1462, 4083, 8717, 1384, 3594, 9719, 9865, 2490, 1779, 507, 9238, 7089, 3997, 5933, 2163, 7126, 4769, 899, 9870, 3457, 9360, 2169, 1518, 1391, 5545, 8604, 9419, 2143, 3632, 4904, 3768, 101, 134, 487, 543, 5172, 1699, 9205, 7702, 3772, 9898, 393, 2383, 3399, 6646, 5356, 1199, 9630, 4107, 4449, 6344, 373, 8083, 4141, 8368, 8961, 4836, 9990, 7036, 1010, 4848, 3863, 4480, 9091, 8413, 9093, 1088, 5164, 5796, 9220, 8856, 3257, 3210, 998, 8077, 608, 5918, 6588, 1111, 4433, 8042, 9677, 1417, 3847, 7205, 4808, 9327, 9212, 2210, 7516, 1653, 638, 6233, 2617, 9753, 8201, 2457, 1666, 3146, 4854, 4139, 2287, 5156, 7841, 6699, 9658, 9784, 9385, 5562, 9810, 6385, 8916, 6109, 1796, 5312, 2020, 2788, 4975, 8601, 2856, 9166, 5350, 6481, 8421, 2725, 7307, 9257, 6480, 5011, 6606, 3862, 8782, 8183, 9456, 2565, 7165, 9711, 4721, 6137, 9665, 1193, 746, 4735, 5501, 229, 9352, 1696, 2595, 3711, 2188, 4631, 367, 2652, 1679, 2965, 3888, 8214, 3644, 123, 3708, 2907, 4766, 5911, 5099, 1215, 5217, 2748, 4870, 8741, 829, 1584, 3189, 1580, 9146, 9697, 6876, 3698, 4206, 590, 1313, 9814, 7232, 7220, 5608, 4267, 6127, 4021, 4529, 6417, 4627, 373, 6197, 280, 508, 9738, 2385, 6347, 5792, 2608, 7595, 1114, 4113, 7773, 4334, 2383, 9533, 3040, 956, 4788, 5220, 632, 7609, 5088, 3383, 8359, 8623, 7967, 718, 2176, 2208, 3516, 9178, 7602, 9105, 4179, 451, 2327, 8105, 8020, 1628, 6384, 3385, 3178, 8984, 2391, 9505, 3941, 1778, 2309, 4350, 609, 9512, 4589, 5687, 378, 5082, 4707, 6120, 6602, 904, 3682, 6692, 2642, 7211, 6720, 8827, 6587, 3520, 8733, 8013, 5755, 4292, 9425, 3869, 8764, 2796, 7151, 1989, 9063, 5203, 4835, 5529, 929, 5879, 2471, 2755, 9813, 9896, 7561, 6248, 1524, 6793, 8442, 6797, 3545, 5707, 7549, 4005, 4111, 4883, 1690, 4599, 6463, 771, 7616, 288, 7676, 4449, 4722, 2295, 7553, 1177, 9121, 7491, 5608, 6137, 3436, 5734, 634, 4562, 5936, 8382, 8018, 1918, 3961, 6626, 2635, 8682, 6786, 4510, 4363, 2727, 4147, 2588, 5248, 5302, 4488, 8737, 2645, 3494, 4729, 4121, 9222, 8417, 6516, 2497, 7136, 8504, 6565, 4366, 1096, 2254, 1831, 4131, 5548, 1376, 2345, 7407, 3090, 2277, 1277, 281, 6729, 2358, 4499, 4908, 4027, 5435, 7032, 9005, 4588, 7720, 9828, 269, 3209, 3612, 8724, 3733, 5547, 2045, 9687, 1687, 1319, 7788, 9474, 2592, 4121, 3159, 1817, 238, 2678, 6747, 5213, 4602, 5682, 2619, 5670, 8162, 9000, 6840, 5150, 5548, 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2658, 1198, 4754, 1866, 9721, 1749, 4543, 9665, 1211, 3246, 992, 5594, 9328, 2951, 837, 8866, 459, 6433, 2958, 7972, 3385, 9927, 2122, 3364, 5625, 6481, 7394, 1947, 7950, 3324, 9291, 2047, 1807, 9243, 2511, 9393, 6229, 1449, 2134, 8017, 9280, 3723, 3863, 6304, 1785, 8074, 9440, 3873, 1630, 5543, 9497, 8924, 1653, 2234, 3901, 1590, 2001, 8052, 4098, 1893, 9893, 2537, 9005, 8935, 9091, 1814, 7106, 6096, 4772, 1202, 5958, 1519, 7841, 3748, 6127, 4669, 2946, 7211, 2521, 8642, 8957, 9126, 5979, 5594, 4548, 2729, 1476, 7908, 5637, 3850, 1220, 262, 8205, 9066, 1881, 7014, 112, 8599, 9569, 4355, 141, 2702, 3566, 5261, 835, 1559, 6005, 2744, 2884, 1877, 7876, 3191, 8236, 2841, 1920, 8312, 3745, 491, 7388, 338, 6824, 8397, 7650, 8069, 1418, 1654, 2499, 6293, 1112, 681, 1576, 601, 2096, 2507, 8803, 6750, 2232, 5219, 3234, 7026, 5712, 2408, 4038, 7663, 1519, 6363, 1849, 4053, 9293, 6632, 3725, 5965, 6885, 4707, 8094, 4997, 8058, 3580, 1976, 625, 5415, 1011, 3522, 5770, 1587, 173, 190, 3401, 5462, 7486, 5308, 4291, 3694, 5053, 2483, 6408, 5660, 5055, 8579, 810, 1250, 4918, 2945, 3188, 6245, 9601, 6953, 8261, 2859, 4528, 4563, 8965, 6931, 6306, 5345, 437, 422, 9647, 2822, 2182, 217, 9174, 7974, 7073, 8264, 1440, 5529, 7674, 4478, 9101, 4019, 570, 4402, 678, 579, 2335, 5610, 2847, 5439, 8642, 5271, 4401, 9143, 5748, 3698, 1044, 5281, 5174, 4528, 6328, 3729, 6646, 8886, 8850, 36, 2299, 1850, 3164, 8132, 489, 9721, 6166, 3985, 2680, 1410, 7098, 5186, 9862, 5690, 5186, 1431, 2350, 6057, 7403, 9323, 9804, 4808, 9301, 5173, 563, 1426, 8893, 7473, 8900, 2997, 771, 3478, 2217, 9903, 7286, 4853, 8445, 1299, 4192, 1393, 1737, 1604, 3210, 2534, 6118, 9011, 9056, 5898, 1762, 9894, 5576, 5753, 7315, 7810, 5147, 9816, 7646, 4613, 7853, 9491, 2655, 7856, 3889, 5132, 6752, 7892, 4236, 2310, 6348, 9983, 4634, 5439, 3682, 1306, 8296, 9567, 6120, 5962, 7877, 9136, 3998, 3255, 2879, 5792, 236, 9665, 7044, 151, 3632, 1209, 8647, 448, 8691, 7383, 1502, 293, 572, 1685, 2982, 4390, 2274, 5836, 9601, 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2964, 6881, 3334, 4239, 9808, 9033, 5279, 5151, 3289, 3575, 5065, 1178, 4594, 2503, 7190, 8307, 9835, 4540, 7153, 9778, 4181, 5746, 1245, 4614, 1506, 6139, 6885, 7374, 4727, 2721, 4348, 231, 3482, 1001, 9040, 9469, 3346, 8414, 3132, 930, 1255, 5658, 6962, 8795, 71, 9991, 1500, 139, 7208, 2704, 5688, 2651, 9595, 7479, 8490, 694, 426, 7222, 6546, 6186, 8041, 924, 2717, 8416, 4261, 1054, 1131, 898, 1314, 845, 6012, 1482, 9534, 5772, 3166, 2028, 3866, 7121, 3178, 8445, 8475, 8109, 8795, 318, 6831, 6245, 4457, 4734, 5056, 5348, 8854, 1294, 8862, 2781, 7900, 8154, 6857, 7399, 2592, 47, 1941, 9402, 7343, 5532, 2672, 7618, 6285, 2487, 7384, 2670, 9761, 9725, 1805, 1759, 562, 4695, 9287, 1162, 6754, 2516, 9814, 3140, 6937, 3451, 2076, 6523, 8607, 6155, 9759, 9096, 3348, 3250, 812, 2059, 2120, 6389, 1037, 8651, 3968, 2909, 4956, 1938, 744, 6227, 4360, 7735, 2888, 7741, 3325, 3705, 9414, 5361, 787, 4649, 3433, 360, 9551, 7366, 6893, 3492, 7063, 1699, 8175, 3948, 9226, 1958, 3198, 6122, 4799, 248, 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2571, 5588, 8033, 3916, 3963, 99, 7356, 9796, 2419, 1317, 5889, 3514, 8127, 9392, 1025, 9727, 8688, 6709, 8985, 7576, 788, 4193, 346, 2510, 1161, 7781, 3820, 3323, 8741, 9420, 5934, 6183, 8685, 7185, 1534, 58, 6402, 7898, 2825, 1234, 2199, 7889, 5520, 6603, 3784, 3045, 8220, 8442, 8109, 8826, 6274, 5500, 7926, 8415, 1720, 5049, 9469, 2386, 6289, 6402, 2578, 7435, 1650, 3031, 9936, 1715, 6431, 9855, 196, 7499, 4680, 6437, 5225, 587, 6334, 6850, 7281, 3170, 8224, 3043, 4297, 4729, 4889, 8036, 673, 7730, 1247, 5007, 1922, 9529, 8566, 2494, 660, 5759, 64, 2349, 3357, 6901, 2370, 98, 2527, 1544, 7353, 8994, 8378, 953, 6561, 3981, 2611, 2612, 8257, 254, 4593, 1560, 7767, 9287, 3567, 920, 7767, 4203, 7363, 548, 320, 2083, 9061, 1158, 9292, 3176, 4131, 4013, 7599, 9700, 5006, 9265, 7556, 6580, 6971, 4433, 8091, 7438, 3416, 220, 169, 6635, 9827, 366, 5818, 6466, 2895, 4554, 3327, 7444, 18, 1164, 3427, 8754, 5599, 8509, 8750, 9356, 9712, 1226, 4566, 3918, 4254, 3678, 455, 7683, 7205, 7968, 1021, 5369, 6480, 1523, 4775, 311, 8493, 3095, 4669, 6878, 1870, 1990, 99, 1898, 5077, 6337, 9198, 7041, 4580, 4894, 9898, 8768, 4594, 2865, 4011, 7766, 7126, 5928, 6095, 2374, 2175, 8339, 5969, 2121, 5076, 4234, 653, 3239, 3213, 9296, 2840, 9226, 4486, 6102, 5092, 7537, 2279, 8920, 2113, 5235, 8554, 4934, 3650, 789, 2202, 7172, 2516, 1518, 6604, 9692, 130, 1550, 6275, 3504, 690, 6625, 3767, 2022, 6101, 4825, 8423, 6268, 6775, 2906, 6433, 54, 4013, 1131, 6660, 6034, 4078, 5158, 5158, 3840, 8638, 4005, 1801, 7025, 8985, 3124, 9753, 6283, 1171, 3572, 5061, 351, 8457, 7607, 8452, 9739, 870, 1462, 7250, 3862, 6054, 7052, 2408, 7864, 7683, 2550, 1244, 9417, 1502, 2682, 7470, 9796, 2713, 6854, 1652, 4484, 9052, 6539, 2098, 1697, 8778, 5096, 2344, 2514, 3563, 4341, 3280, 223, 9857, 3818, 7101, 5039, 5699, 2163, 9074, 4408, 4835, 1478, 7736, 3727, 8518, 7970, 2955, 5611, 3948, 5945, 6000, 1648, 9123, 6259, 146, 4039, 5041, 8904, 7794, 432, 5888, 4293, 2847, 9945, 7758, 9473, 7018, 7211, 9218, 7227, 1029, 2263, 3518, 147, 5403, 2571, 7047, 9193, 8874, 9584, 5928, 8320, 4565, 5, 877, 3584, 7616, 3791, 1147, 4206, 3795, 8332, 5202, 9220, 781, 998, 9665, 8182, 7478, 2850, 2910, 2167, 8183, 8975, 9242, 3644, 5480, 551, 2887, 5167, 3856, 8734, 5056, 5677, 1209, 1601, 540, 7771, 742, 5974, 5957, 8220, 7919, 3763, 3610, 8436, 9353, 4407, 4544, 9704, 9664, 8759, 5511, 5712, 2816, 1001, 4016, 4215, 2372, 9686, 1378, 3914, 2663, 6041, 8862, 9365, 3031, 6012, 3697, 8298, 5523, 5927, 1534, 4091, 9207, 6192, 2245, 5345, 6336, 8908, 4684, 5533, 7246, 6863, 4777, 3438, 4442, 4537, 9233, 5318, 9914, 5468, 4377, 6179, 464, 2980, 7259, 4396, 5169, 2862, 2987, 7866, 4987, 8091, 1869, 5588, 477, 3639, 1236, 3677, 2639, 5456, 3798, 119, 4007, 3411, 7654, 8073, 4430, 8919, 9951, 2527, 3604, 8183, 9866, 9960, 2631, 6540, 633, 7529, 9298, 3707, 8977, 7948, 3147, 2562, 2189, 3758, 7283, 8165, 1277, 569, 3356, 4385, 2587, 1736, 9396, 8961, 8400, 3082, 5020, 2384, 5220, 1142, 3726, 5905, 840, 2496, 2313, 8701, 6342, 8192, 6183, 4862, 2359, 5363, 2935, 654, 3586, 936, 9138, 2627, 5717, 5710, 5169, 476, 6857, 9418, 1879, 9702, 7550, 3908, 5683, 3389, 1616, 5972, 3658, 2136, 8817, 8232, 3123, 6222, 2529, 8793, 876, 1259, 2119, 4313, 7665, 8075, 8105, 609, 4165, 7095, 3725, 5870, 1258, 7652, 5299, 4457, 7043, 7434, 8355, 1857, 5874, 9197, 1408, 5629, 8093, 8301, 7264, 7481, 9555, 1866, 4082, 7644, 4777, 1600, 1908, 3909, 9868, 2230, 9802, 3668, 6954, 9930, 6480, 9569, 5825, 7289, 8361, 5825, 2054, 7360, 8190, 6298, 3942, 8983, 54, 6031, 6812, 805, 6975, 8153, 4169, 1660, 1509, 3895, 4521, 4164, 3841, 8455, 4131, 2832, 7032, 3729, 8203, 3593, 3185, 4690, 8418, 614, 4854, 750, 7607, 3134, 1447, 1500, 1005, 8793, 7009, 1999, 2819, 9384, 9995, 8523, 2973, 5415, 9326, 1676, 8524, 4964, 3932, 4104, 9421, 8570, 4806, 8858, 7671, 8352, 5996, 1820, 3263, 1251, 3380, 9133, 967, 1248, 1009, 4819, 7403, 5808, 9188, 3188, 1760, 2787, 1729, 3056, 8540, 1073, 2321, 8881, 7490, 608, 9386, 3895, 9777, 5169, 6620, 6164, 6050, 5500, 8392, 4210, 260, 4458, 4538, 6515, 1420, 3299, 5380, 9499, 2900, 2737, 6986, 3233, 5290, 3343, 6847, 102, 3305, 4223, 2440, 1758, 3900, 4555, 69, 4373, 1595, 96, 2558, 5780, 417, 4797, 1540, 6829, 5680, 4321, 6035, 3078, 2701, 2299, 1388, 9328, 7199, 6729, 1120, 3911, 9667, 8789, 6699, 1446, 7443, 4029, 7999, 6319, 1010, 8977, 3452, 3424, 5399, 2006, 1832, 6060, 4766, 7597, 2513, 9007, 8490, 8273, 3423, 3826, 8289, 9665, 9960, 8585, 9342, 5104, 3360, 8056, 1262, 7874, 5726, 4729, 9382, 5061, 2203, 3563, 4591, 6351, 4499, 786, 3146, 6932, 3671, 456, 2408, 4429, 9684, 4454, 7679, 1223, 9683, 3349, 1900, 5633, 1685, 8121, 1889, 2514, 6539, 4998, 1191, 1384, 5448, 7191, 2215, 7540, 1998, 6977, 3114, 9719, 5274, 5485, 2001, 994, 7714, 7570, 2798, 5656, 5192, 3617, 7226, 7966, 2575, 6568, 4715, 2109, 2091, 8039, 6915, 1932, 716, 4942, 3819, 6212, 7198, 1380, 6451, 8687, 141, 1025, 4205, 6168, 8697, 2986, 9622, 9318, 6586, 2047, 5703, 7097, 6464, 1150, 6239, 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3704, 8710, 2308, 558, 4674, 8427, 8437, 8169, 9805, 3887, 6052, 6727, 9007, 87, 5597, 5125, 5338, 9642, 2071, 1545, 3895, 1993, 4372, 7033, 861, 8100, 2827, 3422, 8494, 9348, 2001, 9158, 2399, 2584, 8440, 2599, 887, 761, 3183, 7534, 4615, 8362, 206, 5583, 8774, 4244, 4080, 4733, 5814, 3498, 1214, 3027, 5108, 1161, 1692, 9565, 6854, 3480, 6241, 2682, 7159, 529, 6981, 9953, 4091, 6324, 751, 9938, 7531, 5210, 9368, 1243, 337, 9083, 9564, 7165, 1994, 569, 5772, 6234, 82, 1228, 6112, 2264, 3154, 852, 9292, 4693, 6833, 5391, 9771, 9803, 2082, 1656, 2918, 3141, 5684, 3531, 35, 2032, 8405, 3231, 7114, 5244, 3144, 1615, 4423, 5575, 4224, 5458, 7692, 425, 1560, 4666, 3147, 4511, 3492, 3259, 394, 1454, 7319, 8698, 675, 7021, 3933, 2754, 8441, 4276, 7541, 6462, 5380, 6851, 1257, 4479, 7864, 9462, 279, 393, 8117, 7138, 3693, 188, 7413, 7836, 9854, 3353, 7753, 1526, 5483, 5039, 5852, 841, 7323, 3073, 9501, 281, 9509, 4058, 164, 8371, 8763, 971, 8017, 4580, 3212, 980, 3717, 8116, 5056, 4910, 7095, 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8013, 7350, 9977, 4847, 8426, 1441, 508, 3433, 9339, 6865, 1112, 5508, 5881, 1408, 7698, 3770, 6237, 4363, 868, 5722, 8662, 7298, 6255, 4014, 6612, 6354, 2346, 4918, 724, 2272, 9512, 1647, 1751, 7290, 7885, 1676, 7080, 7228, 268, 1723, 5741, 4547, 6617, 8794, 4137, 7641, 9951, 8767, 6095, 9638, 7322, 3574, 6106, 8905, 2453, 2950, 9014, 9016, 6218, 1266, 9901, 2069, 2259, 7929, 1482, 165, 3895, 8729, 9149, 370, 3830, 9432, 9440, 3795, 3678, 5292, 1503, 9306, 6767, 2218, 4284, 4511, 2505, 5910, 2776, 5068, 7671, 3003, 5961, 157, 5554, 3083, 7357, 996, 5979, 9845, 6935, 1091, 5638, 754, 1427, 3828, 3913, 2838, 3336, 3749, 9713, 7137, 872, 7760, 6419, 8718, 4832, 9459, 8950, 5686, 4833, 6917, 3872, 5191, 6612, 4052, 8619, 6728, 2256, 9587, 4354, 6741, 1058, 3361, 8036, 6275, 5854, 5996, 8328, 7730, 5617, 1276, 7786, 7018, 7538, 887, 5567, 6880, 3241, 7724, 906, 8589, 5169, 95, 8167, 2103, 4697, 655, 8003, 4752, 7990, 5168, 5717, 3132, 4427, 6292, 3437, 2170, 5925, 1514, 6575, 2157, 3958, 5914, 9511, 412, 221, 7250, 372, 6521, 4553, 3114, 6125, 2388, 6185, 5266, 6183, 8695, 9927, 9649, 9260, 3776, 8690, 866, 9797, 9301, 1945, 1153, 8954, 6727, 2888, 4818, 8031, 3176, 1883, 2605, 1259, 3089, 3960, 9937, 4293, 3685, 1308, 1717, 3889, 9420, 5316, 100, 6440, 9995, 8635, 8338, 5179, 804, 3857, 4485, 9601, 3988, 3779, 5452, 7707, 7403, 7950, 9574, 9841, 6630, 7810, 666, 7252, 9341, 7613, 3781, 666, 7092, 643, 6642, 479, 3592, 304, 7992, 1377, 4003, 1985, 7493, 6655, 8460, 4588, 9600, 7348, 4781, 4750, 3514, 6532, 7645, 3480, 8167, 7119, 3956, 1505, 7991, 917, 7275, 3780, 7584, 6795, 8201, 892, 698, 8003, 8004, 4486, 2837, 268, 8476, 3669, 8571, 4327, 2362, 5448, 8905, 3473, 6107, 7663, 4490, 1265, 3891, 9884, 445, 6800, 7307, 9753, 2163, 7210, 4972, 2797, 3526, 2036, 8801, 4837, 8955, 9077, 4007, 1449, 849, 462, 3274, 995, 1254, 6807, 796, 2942, 8944, 1920, 4349, 672, 8945, 7630, 7888, 2184, 736, 7884, 5367, 8344, 5213, 8560, 9089, 1489, 1661, 2405, 6842, 3393, 8866, 6240, 7626, 3425, 3229, 1050, 7882, 8769, 7805, 2064, 5028, 330, 4528, 8091, 4256, 9980, 798, 8341, 5800, 5296, 7990, 4584, 1019, 6373, 664, 1679, 3194, 521, 5549, 973, 6378, 9459, 3555, 236, 1389, 3439, 5626, 4600, 3521, 9513, 7213, 372, 9371, 312, 3091, 8909, 2425, 9034, 8107, 6014, 6509, 7678, 9893, 8477, 3498, 6407, 1612, 6076, 4465, 8940, 7384, 1606, 5883, 5602, 4951, 3548, 1640, 9386, 5924, 6175, 3712, 1965, 6474, 3254, 1832, 809, 5854, 4746, 5000, 9534, 290, 3525, 6908, 5757, 9035, 4428, 8341, 6480, 1763, 3422, 1560, 7329, 520, 7797, 1756, 9946, 2406, 421, 4545, 9520, 6848, 8840, 1443, 7484, 4842, 4518, 2379, 5265, 9535, 6110, 2626, 4539, 6067, 8270, 2708, 2143, 3695, 7916, 2422, 2485, 6161, 4669, 5014, 9982, 6510, 6131, 6266, 2225, 4194, 5067, 6877, 4370, 9689, 9472, 3903, 6576, 96, 4732, 538, 6957, 1129, 8291, 3942, 5746, 9350, 9023, 6958, 3693, 3383, 2519, 4195, 9837, 7839, 9887, 1174, 1920, 5585, 1862, 5304, 1230, 4971, 9723, 6103, 3972, 4517, 2161, 5941, 7762, 7304, 3889, 7308, 4288, 3141, 4841, 3013, 5379, 337, 5512, 7551, 8601, 646, 7611, 7960, 3111, 3278, 6796, 854, 1549, 4802, 9507, 5509, 2199, 1467, 3990, 5313, 3881, 5567, 5071, 2206, 7895, 3142, 6664, 584, 7138, 5493, 8255, 8742, 1622, 5838, 2050, 7210, 4910, 2968, 7721, 1285, 4375, 8832, 8767, 2347, 7143, 7201, 4093, 6676, 8100, 646, 9436, 3177, 3426, 1679, 3393, 3125, 6627, 9531, 2634, 9689, 6625, 7609, 6899, 9945, 403, 8026, 8968, 3827, 1077, 3024, 3064, 2052, 1625, 1061, 853, 8383, 8891, 6849, 9013, 2559, 5060, 2856, 5031, 2643, 5127, 3163, 9953, 6148, 5924, 1394, 5728, 1866, 1683, 5649, 6724, 9329, 6928, 6277, 8022, 3460, 6069, 8290, 4812, 2917, 4069, 3653, 6162, 6488, 6990, 3041, 5331, 700, 6131, 2300, 5936, 5089, 8734, 5446, 5262, 1786, 3213, 3770, 3992, 6694, 1732, 2591, 3750, 455, 6000, 5088, 9657, 4082, 6887, 223, 2121, 6506, 2871, 483, 8158, 936, 5429, 8965, 1674, 9505, 7094, 3430, 9654, 7599, 8284, 5908, 8098, 1000, 2634, 966, 8163, 6479, 1824, 1188, 7018, 2228, 5654, 2734, 7227, 7934, 7688, 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2322, 3905, 6062, 5263, 2260, 6278, 7794, 8521, 7287, 5891, 1561, 3708, 1913, 9965, 5850, 7361, 6831, 1388, 724, 3729, 3786, 7973, 2680, 1210, 8171, 5323, 1321, 7922, 6, 7762, 9613, 1603, 2334, 7376, 6509, 7682, 2, 149, 2151, 5248, 6084, 8277, 2743, 2540, 5809, 9408, 336, 7843, 2125, 795, 3667, 8658, 8667, 2264, 762, 2193, 9076, 6341, 9641, 875, 9794, 6686, 609, 713, 1705, 7264, 4605, 9099, 6263, 3490, 6880, 6218, 4967, 1747, 6945, 2975, 2131, 2733, 6059, 1318, 905, 8663, 1464, 3928, 3906, 310, 3179, 8998, 7411, 3562, 3870, 6442, 7646, 334, 2840, 1348, 1449, 8305, 8242, 8689, 9680, 2970, 9782, 8329, 2664, 9835, 8083, 3538, 7374, 1503, 4913, 5185, 4948, 5216, 3899, 711, 1186, 1692, 9469, 4796, 2106, 5447, 8843, 6965, 9134, 9568, 9119, 6968, 9867, 609, 4954, 4833, 4965, 1990, 7445, 8811, 2436, 970, 3068, 4047, 2171, 8377, 1157, 4186, 5919, 732, 3486, 4537, 2519, 592, 2551, 5280, 9870, 7631, 6172, 2185, 1929, 6173, 4290, 9036, 2418, 3148, 6019, 2981, 28, 6332, 3214, 1165, 1985, 4622, 6826, 8133, 4711, 1099, 9854, 5839, 9875, 1464, 9305, 4366, 9757, 2234, 9500, 932, 9274, 7501, 8975, 9384, 4321, 6831], 117])

def generate_case(nums):
    l = []
    t = []
    target_s = random.randint(10, 120)
    for i in range(nums):
        interval = random.randint(100, 10000)
        dist = sum(l) + interval
        r_t = random.randint(1,9999)
        while not is_green(target_s, dist, r_t):
            r_t = random.randint(1, 9999)
        l.append(interval)
        t.append(r_t)
    return [l, t, target_s]

def generate_random_case():
    nums = random.randint(10,20)
    l = []
    t = []
    target_s = random.randint(10, 90)
    for i in range(nums):
        interval = random.randint(100, 10000)
        dist = sum(l) + interval
        r_t = random.randint(1,9999)
        while True:
            if not is_green(target_s, dist, r_t):
                r_t = random.randint(1, 9999)
            else:
                l.append(interval)
                t.append(r_t)
                if max_speed(l, t) == target_s:
                    break
                else:
                    r_t = random.randint(1, 9999)
    return [l, t, target_s]

random_cases = []
for i in range(30):
    random_case = generate_case(30)
    if max_speed(random_case[0], random_case[1]) == random_case[2]:
        random_cases.append(random_case)

s = Solution()
for c in random_cases:
    if s.answer(c[0], c[1]) != c[2]:
        print("Error for case l=%s, t=%s", str(c[0]), str(c[1]))
        exit(1)

for c in cases:
    if s.answer(c[0], c[1]) != c[2]:
        if len(c[0]) == 1:
            print("Certain case failed.")
        else:
            print("Error for case l=%s, t=%s", str(c[0]), str(c[1]))
        exit(1)

exit(0)
